The following abbreviations will be employed in the following description of the background art and in the description of the presently preferred embodiments of this invention:    BIBO: bounded-input bounded-output    BLER: block error rate    BLUE: best linear unbiased estimator    cFIR: chip finite impulse response    EKF: extended Kalman filter    FIR: finite-impulse response    KF: Kalman filter    LMMSE: linear minimum mean squared error    MIMO: multiple input multiple output    MMSE: minimum mean squared error    SISO: single input single output    swRLS: sliding window recursive least squares    QAM: quadrature amplitude modulation.    QPSK: quadrature phase shift key
Channel equalization is necessary for improving the performance of downlink CDMA receivers. The existence of a multipath channel destroys the orthogonality among the spreading codes, as clearly seen from the fact that the RAKE receiver in many cases reaches a noise floor at a frame error rate above 0.1. One of the simplest ways of improving the receiver performance, for downlink single-user detection, is to restore the code orthogonality. This is motivated in part by the fact that in single-user detection the receiver does not know the spreading codes of the interfering users, which are required by some of the previously proposed multi-user detection techniques of the prior art.
Well-known methods in the literature for orthogonality restoration rely on LMMSE FIR equalizers, realized either at the chip level or the symbol level. These equalizers may be provided in an adaptive or in a non-adaptive/block form. The block implementation requires a matrix inversion for every segment of data over which the observation sequence is considered stationary. Frequent matrix inversions may, however, impose a severe computational burden on the receiver.
The symbol-level LMMSE equalizer of T. P. Krauss, W. J. Hillery, and M. D. Zoltowsky, “MMSE equalization for forward link in 3G CDMA: symbol-level versus chip-level,” Tenth IEEE workshop on Stat. Signal and Array Proc., 2000 requires one matrix inversion per segment. This equalizer, in essence, is a chip-level LMMSE equalizer that incorporates the descrambling and the despreading operations, typically done outside of the equalizer. Its objective, however, is to minimize the error variance of the symbol estimate rather than of the chip estimate. On the other hand, matrix inversion can be avoided totally by means of adaptive equalizers. Adaptive implementations can be performed in a number of ways. A well-known technique uses the stochastic gradient algorithm, from which the Griffiths algorithm is derived by replacing the covariance matrix with a rank-1 approximation. However, stochastic gradient-based algorithms suffer from slow convergence and tend to be unreliable. A better alternative is to update the covariance matrix continually in the weighted-average recursive fashion R(t+1)=λR(t)+(1−λ)y(t+1)yH(t+1) which has an adaptive inverse form, with v(l) being the forgetting factor. In many cases, however, even this recursion is not sufficiently reliable.
The Kalman filter (KF) is a powerful statistical method suitable for the estimation/tracking of not only stationary but also non-stationary processes. Reference in this regard can be made to M. H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons, Inc.: New York, N.Y., 1996, and to R. E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME, J. Basic Engineering, ser. 82D, pp. 35-45, March 1960. Several authors, most notably Iltis et al (R. A. Iltis and L. Mailaender, “An adaptive multiuser detector with joint amplitude and delay estimation,” IEEE J. Selected Areas in Com., vol. 12, pp. 774-85, June 1994, and R. A. Iltis, “Joint estimation of PN code delay and multipath using the extended Kalman filter,” IEEE Trans. Com., vol. 38, pp. 1677-85, October 1990) may have used Kalman filtering for joint signal detection and parameter estimation. It can be noted in this regard that these authors use the extended Kalman filter (EKF) for amplitude and delay estimation. The true state-space formulation involving delay parameters manifests a nonlinear system, due to the fact that the observation is nonlinear with respect to the delays. Hence, the basic principle of the EKF is to linearize the observation equation, by means of the first-order Taylor series expansion; the state dynamics is described by imposing a Gauss-Markov model onto the state evolution. More work of this nature on delay estimation using the EKF can be found in T. J. Lim and L. K. Rasmussen, “Adaptive symbol and parameter estimation in asynchronous multiuser CDMA detectors,” IEEE Trans. on Com., vol. 45, pp. 213-20, February 1997; R. A. Iltis, “A DS-CDMA tracking mode receiver with joint channel/delay estimation and MMSE detection,” IEEE Trans. on Com., vol. 49, pp. 1770-9, October 2001; and in K. J. Kim and R. A. Iltis, “Joint detection and channel estimation algorithms for QS-CDMA signals over time-varying channels,” IEEE Trans. on Com., vol. 50, pp. 845-55, May 2002.
Other authors have discussed techniques that are more relevant to CDMA downlink equalization than the above-mentioned references: T. J. Lim, L. K. Rasmussen, and H. Sugimoto, “An asynchronous multiuser CDMA detector based on the Kalman filter,” IEEE J. on Select. Areas in Com., vol. 16, pp. 1711-22, December 1998; T. J. Lim and Y. Ma, “The Kalman filter as the optimal linear minimum mean-squared error multiuser CDMA detector,” IEEE Trans. Info. Theory, vol. 46, pp. 2561-6, November 2000; Z. Xu and T. Wang, “Blind detection of CDMA signals based on Kalman filter,” in Record of the 35th Asilomar Conf. on Signals, Systems and Computers, vol. 2, pp. 1545-9, 2001; and L.-M. Chen, B.-S. Chen, and W.-S. Hou, “Adaptive multiuser DFE with Kalman channel estimation for DS-CDMA systems in multipath fading channels,” Elsevier Signal Processing, vol. 81, pp. 713-33, 2001. Most interesting perhaps is the state-space formulation of T. J. Lim, L. K. Rasmussen, and H. Sugimoto, “An asynchronous multiuser CDMA detector based on the Kalman filter,” IEEE J. on Select. Areas in Com., vol. 16, pp. 1711-22, December 1998. In this formulation, each element of the state vector includes the channel taps and the transmitted symbols of all users. What makes this formulation interesting, in particular, is the fact that it yields the symbol estimate (rather than the chip estimate). The KF for this model operates at the chip level (rather than at the symbol level); and such a strategy avoids matrix inversion in computing the Kalman gain, while taking advantage of the ability of the KF to handle nonstationary dynamics, i.e., a time-varying state-dynamics matrix.
Another state-space formulation of interest is presented in T. J. Lim and Y. Ma, “The Kalman filter as the optimal linear minimum mean-squared error multiuser CDMA detector,” IEEE Trans. Info. Theory, vol. 46, pp. 2561-6, November 2000, where the state vector consists of all users' transmitted symbols at the current time epoch, and the measurement matrix is the product of the channel matrix and one consisting of the spreading codes. This formulation leads to a state-space model that requires a matrix inversion per symbol interval; and the size of the Hermitian matrix to be inverted is no less than the processing gain. A state-space model similar to the one proposed by T. J. Lim and Y. Ma can be found in L.-M. Chen, B.-S. Chen, and W.-S. Hou, “Adaptive multiuser DFE with Kalman channel estimation for DS-CDMA systems in multipath fading channels,” Elsevier Signal Processing, vol. 81, pp. 713-33, 2001. Other state-space formulations can be found in L.-M. Chen, B.-S. Chen, and W.-S. Hou, “Adaptive multiuser DFE with Kalman channel estimation for DS-CDMA systems in multipath fading channels,” Elsevier Signal Processing, vol. 81, pp. 713-33, 2001, and in R. Chen, X. Wang, and J. S. Liu, “Adaptive joint detection and decoding in flat-fading channels via mixture Kalman filtering,” IEEE Trans. Info. Theory, vol. 46, pp. 2079-94, September 2000, which impose linear statistical dynamic models onto the channel.
In conclusion, all of the above-mentioned state-space formulations require knowledge of all users' spreading codes, making them suitable for multi-user detection but inappropriate for single-user detection.
In general, the problem was approached in the prior art by employing either of the following frameworks: (i) multi-user detection (linear or nonlinear, the latter more complicated and having better error performance) which requires knowledge of all user codes and has a complexity that increases with the number of users, and (ii) single-user detection with variants of FIR LMMSE equalizers that restores the orthogonality of user codes.
A need thus exists to provide a state-space approach, either at the symbol level or the chip level, that is well-suited for single-user detection in a CDMA downlink receiver.